Transcript PPadua-Douglas,E. CNM 2011-11-02 8847

October 31, 2011
At the end of today, you will be able to:
Solve linear equations by graphing.
Determine what each system indicates about their
solutions.
HW 3.1&3.2 Pg. 113 #13-17, 25,27
y
odds, Pg. 120 #13-17 odds
Graph y = 2x – 3
5
-3
1: Start at___________
2
2: (up or down)____steps
1
3: right______step
4: Plot the point, and continue -5
steps #1-4 to find more points.
5: Draw the line that goes
through the points.
-5
6: Label the line.
x
5
Use a straight edge, graph paper, and
two different colored pencils to graph
the following:
1. Graph two of the lines on the same
graph:
y = x – 1 and y = -x – 3
2. Graph:
1
y  x  3 and
2
3. Graph: y = -2x + 4 and
1
y  x 1
2
4
y  x4
2
What do the graphs of
System of Equations tell you?
Intersecting
Lines
Exactly one
solution
Consistent and
independent
Parallel
Lines
No solution
Inconsistent
Same
Line
Infinitely
many solutions
Consistent and
dependent
A solution of the system of
equations is the ordered pair where
the two lines intersect.
What point did the two lines in #1 intersect?
So, (-1, -2) is the solution for the system:
y = x – 1 and
y = -x – 3
Example 1: Solve the system by
*If the equations
graphing.
2x + y = -7
x–y=1
are in standard
form, find the xy-intercepts.
2x + y = -6
x–y=1
x-int (-3, 0)
x-int (1, 0)
y-int (0, -6)
y-int (0,-1)
Example 2: Graph the system and describe
it as a consistent and independent,
consistent and dependent, or inconsistent.
6x + 8y = -16
3
y   x 2
4
Use Slope Intercept Form or find the x-yintercepts

How does a system of equations work?
Figure out the ages for:
,
if,
,
+
= 16
=5
+
−
=1
Example 1: Solve using Substitution
x + 2y = 8
1
Step 1:
x  y  18
Isolate one of
2
the variables.
Step 2:
Substitute the

value of the
variable in the
2nd equation.
Step 3:

Simplify and
solve for the

variable.
x = 8 – 2y
1
(8  2y)  y  18
2
4  y  y  18
4 – 2y = 18
-4
-4
-2y = 14
y = -7
Wait! You’re
not done,
what does x
equal?
Example 1 continued:
x + 2y = 8
1
x  y  18
2
Step 4: Substitute
again into one of the
equations to solve for
the other variable.

Since y = -7,
x + 2(-7) = 8
x - 14 = 8
+14 +14
x = 22
The solution to the system is x = 22 and y = -7, or
(22, -7)
Practice
Solve using substitution
1. 4c + 2d = 10
c + 3d = 10
2. 4x – 3y = 1
y=x+4
3. y = 4x – 5
y = 8 – 2x